So yes, entrenched actors (i.e. coal companies) will react to a rise in the price of coal by mining for more coal. However, many other actors will be incentivized to innovate and develop new sources of energy.
More expensive coal can help speed the process, I certainly agree with that. The question is, can you buy enough coal mines around the world to crash the coal industry in that respect, and out-pace the amount of new coal supply other miners can bring to the market seeking higher profits. I seriously doubt it, I'd argue there's far too much coal.
Politically you'd have to basically use the Obama Admin tactics, globally, to hit the coal industry, while also removing as many mines as possible. It's an incredibly expensive, risky proposition (and good luck getting everyone to sign on to it) - when we'd be far better off continuing to improve alt energy, and building nuclear plants. China for example isn't going to chop their own legs off to placate climate concerns, they're going to keep using coal until they can gradually diversify to other sources like nuclear, wind and solar.